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Previous GATE
0
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1
GATE2017240
A person decides to toss a fair coin repeatedly until he gets a head. He will make at most $3$ tosses. Let the random variable $Y$ denote the number of heads. The value of $\text{var} \{Y\}$, where $\text{var} \{ \cdot \}$ denotes the variance, equals $\frac{7}{8} \\$ $\frac{49}{64} \\$ $\frac{7}{64} \\$ $\frac{105}{64}$
asked
Feb 27, 2017
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Arjun
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5.4k
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gate2017ee2
0
votes
0
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2
GATE2015252
The following discretetime equations result from the numerical integration of the differential equations of an undamped simple harmonic oscillator with state variables $x$ and $y$. The integration time step is $h$. $\frac{x_{k+1}x_{k}}{h}=y_{k}$ ... stable for $0 < h <\frac{1}{2\pi}$ The system is stable for $\frac{1}{2\pi}<h<\frac{1}{\pi}$
asked
Feb 12, 2017
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by
makhdoom ghaya
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9.2k
points)
gate2015ee2
0
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0
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3
GATE2017214
A $3$phase, $4$pole, $400$V, $50$Hz squirrelcage induction motor is operating at a slip of $0.02$. The speed of the rotor flux in mechanical rad/sec, sensed by a stationary observer, is closest to $1500$ $1470$ $157$ $154$
asked
Feb 27, 2017
in
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by
Arjun
(
5.4k
points)
gate2017ee2
0
votes
0
answers
4
GATE2017255
A thin soap bubble of radius $R=1$ cm, and thickness $a=3.3 \mu m (a << R)$, is at a potential of $1$ V with respect to a reference point at infinity. The bubble bursts and becomes a single spherical drop of a soap (assuming ... , of the resulting single spherical drop with respect to the same reference point at infinity is _________. (Give the answer up to two decimal places.)
asked
Feb 27, 2017
in
new
by
Arjun
(
5.4k
points)
gate2017ee2
numericalanswers
0
votes
1
answer
5
GATE201814
In the logic circuit shown in the figure, $Y$ is given by $Y=ABCD$ $Y=(A+B)(C+D)$ $Y=A+B+C+D$ $Y=AB+CD$
asked
Feb 19, 2018
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new
by
Arjun
(
5.4k
points)
gate2018ee
0
votes
0
answers
6
GATE2015150
A $200/400$ V, $50$ Hz, twowinding transformer is rated at $20$ kVA. Its windings are connected as an autotransformer of rating $200/600$ V. A resistive load of $12 \Omega$ is connected to the high voltage ($600$ V) side of the autotransformer. The value of equivalent load resistance (in Ohm) as seen from low voltage side is _________.
asked
Feb 12, 2017
in
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by
makhdoom ghaya
(
9.2k
points)
gate2015ee1
twowinding
transformer
autotransformer
numericalanswers
0
votes
0
answers
7
GATE20184
Four power semiconductor devices are shown in the figure along with their relevant terminals. The device(s) that can carry dc current continuously in the direction shown when gated appropriately is (are) Triac only Triac and MOSFET Triac and GTO Thyristor and Triac
asked
Feb 19, 2018
in
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Arjun
(
5.4k
points)
gate2018ee
0
votes
0
answers
8
GATE2017249
For the synchronous sequential circuit shown below, the output $Z$ is zero for the initial conditions $Q_{A}, Q_{B}, Q_{C}= Q'_{A}, Q'_{B}, Q'_{C}=100$ The minimum number of clock cycles after which the output $Z$ would again become zero is _________.
asked
Feb 27, 2017
in
new
by
Arjun
(
5.4k
points)
gate2017ee2
numericalanswers
0
votes
0
answers
9
GATE201851
A $3$phase $900$ kVA, $3 \: kV/ \sqrt{3} kV$ ( $\Delta/$), $50$ Hz transformer has primary (high voltage side) resistance per phase of $0.3 \: \Omega$ and secondary (low voltage side) resistance per phase of $0.02 \: \Omega$. Iron loss of the transformer is $10 \: kW$. The full load $\%$ efficiency of the transformer operated at unity power factor is _______ (up to $2$ decimal places)
asked
Feb 19, 2018
in
new
by
Arjun
(
5.4k
points)
gate2018ee
numericalanswers
+1
vote
1
answer
10
GATE201721
An urn contains $5$ red balls and $5$ black balls. In the first draw, one ball is picked at random and discarded without noticing its colour. The probability to get a Red ball in the second draw is $\frac{1}{2} \\$ $\frac{4}{9} \\$ $\frac{5}{9} \\$ $\frac{6}{9} $
asked
Feb 27, 2017
in
new
by
Arjun
(
5.4k
points)
gate2017ee2
0
votes
0
answers
11
GATE2019 EE: 39
If $\textbf{A}= 2x \textbf{i} + 3y \textbf{j} +4z \textbf{k}$ and $u=x^2+y^2+z^2$, then $\text{div} \big(u \textbf{A} \big)$ at $(1,1,1)$ is _______
asked
Feb 12
in
new
by
Arjun
(
5.4k
points)
gate2019ee
numericalanswers
0
votes
0
answers
12
GATE201714
A solid iron cylinder is placed in a region containing a uniform magnetic field such that the cylinder axis is parallel to the magnetic field direction. The magnetic field lines inside the cylinder will Bend closer to the cylinder axis Bend farther away from the axis Remain uniform as before Cease to exist inside the cylinder
asked
Feb 27, 2017
in
new
by
Arjun
(
5.4k
points)
gate2017ee1
0
votes
0
answers
13
GATE2017224
The nominal $\pi$ circuit of a transmission line is shown in the figure. Impedance $Z=100 \angle 80^{\circ} \Omega$ and reactance $X=3300 \Omega$. The magnitude of the characteristic impedance of the transmission line, in $\Omega$, is __________. (Give the answer up to one decimal place.)
asked
Feb 27, 2017
in
new
by
Arjun
(
5.4k
points)
gate2017ee2
numericalanswers
0
votes
0
answers
14
GATE201818
Let $f$ be a realvalued function of a real variable defined as $f(x)=x – [x]$, where $[x]$ denotes the largest integer less than or equal to $x$. The value of $\int_{0.25}^{1.25} f(x) dx$ is _______ (up to $2$ decimal places).
asked
Feb 19, 2018
in
new
by
Arjun
(
5.4k
points)
gate2018ee
numericalanswers
0
votes
1
answer
15
GATE201852
A $200$ V DC series motor, when operating from rated voltage while driving a certain load, draws $10$ A current and runs at $1000$ r.p.m. The total series resistance is $1 \: \Omega$. The magnetic circuit is assumed to be linear. At the same supply voltage, the load torque is increased by $44 \%$. The speed of the motor in r.p.m (rounded to the nearest integer) is _____________
asked
Feb 19, 2018
in
new
by
Arjun
(
5.4k
points)
gate2018ee
numericalanswers
0
votes
0
answers
16
GATE201850
The figure shows two buck converters connected in parallel. The common input dc voltage for the converters has a value of $100 \: V$. The converters have inductors of identical value. The load resistance is $1 \: \Omega$. The capacitor voltage has negligible ripple. Both ... average value of $i_{s1}$, the current of switch $S1$ (in Ampere), is ____________ (up to $2$ decimal places).
asked
Feb 19, 2018
in
new
by
Arjun
(
5.4k
points)
gate2018ee
numericalanswers
0
votes
0
answers
17
GATE2019 EE: 20
A coaxial Cylindrical capacitor is shown in the Figure(i) has dielectric with relative permittivity $\varepsilon_{r1} = 2$. When one – fourth portion of the dielectric is replaced with another dielectric of relative permittivity $\varepsilon_{r2}$, as shown in the Figure(ii), the capacitance is doubled. The value of $\varepsilon_{r2}$ is _________.
asked
Feb 12
in
new
by
Arjun
(
5.4k
points)
gate2019ee
numericalanswers
0
votes
0
answers
18
GATE201854
The equivalent circuit of a single phase induction motor is shown in the figure, where the parameters are $R_1 =R_2=X_{l1}=X_{l2} = 12 \Omega$, $X_M=240 \: \Omega$ and $S$ is the slip. At noload, the motor speed can be approximated to the synchronous speed. The noload lagging power factor of the motor is __________ (up to $3$ decimal places).
asked
Feb 19, 2018
in
new
by
Arjun
(
5.4k
points)
gate2018ee
numericalanswers
0
votes
0
answers
19
GATE201841
In the circuit shown in the figure, the bipolar junction transistor (BJT) has a current gain $\beta = 100$. The baseemitter voltage drop is a constant, $V_{BE}=0.7 \: V$. The value of the Thevenin equivalent resistance $R_{Th}$ (in $\Omega$) as shown in the figure is _________ (up to $2$ decimal places)
asked
Feb 19, 2018
in
new
by
Arjun
(
5.4k
points)
gate2018ee
numericalanswers
0
votes
0
answers
20
GATE2017151
Consider a causal and stable $LTI$ system with rational transfer function $H(z)$, whose corresponding impulse response begins at $n=0$. Furthermore, $H(1)=\frac{5}{4}$. The poles of $H(z)$ are $p_{k}=\frac{1}{\sqrt{2}} \text{exp}(j\frac{(2k1)\pi}{4})$ ... all at $z=0$. Let $g[n]=j^{n}h[n]$. The value of $g[8]$ equals __________. (Give the answer up to three decimal places.)
asked
Feb 27, 2017
in
new
by
Arjun
(
5.4k
points)
gate2017ee1
numericalanswers
0
votes
0
answers
21
GATE201844
Let $A= \begin{bmatrix} 1 & 0 & 1 \\ 1 & 2 & 0 \\ 0 & 0 & 2 \end{bmatrix}$ and $B=A^3A^24A+5I$, where $I$ is the $3 \times 3$ identify matrix. The determinant of $B$ is _______ (up to $1$ decimal place).
asked
Feb 19, 2018
in
new
by
Arjun
(
5.4k
points)
gate2018ee
numericalanswers
0
votes
0
answers
22
GATE2019 EE: 49
A threephase $50$ Hz, $400$ kV transmission line is $300$ km long. The line inductance is $1$ mH/km per phase, and the capacitance is $0.01 \: \mu F/km$ per phase. The line is under open circuit condition at the receiving end and energized with $400$ kV at the sending end, the receiving end line voltage in kV (round off to two decimal places) will be _________
asked
Feb 12
in
new
by
Arjun
(
5.4k
points)
gate2019ee
numericalanswers
0
votes
0
answers
23
GATE2017144
The magnitude of magnetic flux density (B) in micro Teslas $(\mu T)$, at the centre of a loop of wire wound as a regular hexagon of side length $1 m$ carrying a current $(I=1 A)$, and placed in vacuum as shown in the figure is _________. (Give the answer up to two decimal places.)
asked
Feb 27, 2017
in
new
by
Arjun
(
5.4k
points)
gate2017ee1
numericalanswers
0
votes
0
answers
24
GATE2019 EE: 28
A periodic function $f(t)$, with a period of $2 \pi$, is represented as its Fourier series, $f(t) = a_0 + \sum_{n=1}^{\infty }a_n \cos nt + \sum_{n=1}^{\infty} b_n \sin nt.$ ... $a_1 = \frac{A}{2}; \: b_1 = 0$ $a_1 = 0; \: b_1 = \frac{A}{\pi}$ $a_1 = 0;b_1 = \frac{A}{2}$
asked
Feb 12
in
new
by
Arjun
(
5.4k
points)
gate2019ee
0
votes
0
answers
25
GATE201853
A dc to dc converter shown in the figure is charging a battery bank, $B2$ whose voltage is constant at $150 \: V$. $B1$ is another battery bank whose voltage is constant at $50 \: V$. The value of the inductor, $L$ is $5$ ... state and assuming the diode D to be ideal, the power transferred from $B1$ to $B2$ (in Watt) is ___________ (up to $2$ decimal places)
asked
Feb 19, 2018
in
new
by
Arjun
(
5.4k
points)
gate2018ee
numericalanswers
0
votes
0
answers
26
GATE201810
A positive charge of $1$ nC is placed at $(0,0,0.2)$ where all dimensions are in meters. Consider the $xy$ plane to be a conducting ground plane. Take $\epsilon_0 = 8.85 \times 10^{12}$ F/m. The $Z$ component of the E field at $(0,0,0.1)$ is closest to $899.18$ V/m $899.18$ V/m $999.09$ V/m $999.09$ V/m
asked
Feb 19, 2018
in
new
by
Arjun
(
5.4k
points)
gate2018ee
0
votes
1
answer
27
GATE2019 EE: 2
$M$ is $2 \times 2$ matrix with eigenvalues $4$ and $9.$ The eigenvalues of $M^{2}$ are $4$ and $9$ $2$ and $3$ $2$ and $3$ $16$ and $81$
asked
Feb 12
in
new
by
Arjun
(
5.4k
points)
gate2019ee
0
votes
0
answers
28
GATE2019 EE: 10
The parameter of an equivalent circuit of a threephase induction motor affected by reducing the rms value of the supply voltage at the rated frequency is rotor resistance rotor leakage reactance magnetizing reactance stator resistance
asked
Feb 12
in
new
by
Arjun
(
5.4k
points)
gate2019ee
0
votes
0
answers
29
GATE201855
The voltage $v(t)$ across the terminals $a$ and $b$ as shown in the figure, is a sinusoidal voltage having a frequency $\omega = 100 \text{ radian/s}$. When the inductor current $i(t)$ is in phase with the voltage $v(t)$, the magnitude of the impedance $Z$ (in $\Omega$) seen between the terminals $a$ and $b$ is __________ (up to $2$ decimal places)
asked
Feb 19, 2018
in
new
by
Arjun
(
5.4k
points)
gate2018ee
numericalanswers
0
votes
0
answers
30
GATE201846
The unit step response $y(t)$ of a unity feedback system with open loop transfer function $G(s)H(s)= \frac{K}{(s+1)^2(s+2)}$ is shown in the figure. The value of $K$ is ___________ (up to $2$ decimal places).
asked
Feb 19, 2018
in
new
by
Arjun
(
5.4k
points)
gate2018ee
numericalanswers
0
votes
0
answers
31
GATE2017137
The logical gate implemented using the circuit shown below where $V_{1}$ and $V_{2}$ are inputs (with $0$V as digital $0$ and $5$V as digital $1$) and $V_{out}$ is the output, is NOT NOR NAND XOR
asked
Feb 27, 2017
in
new
by
Arjun
(
5.4k
points)
gate2017ee1
0
votes
0
answers
32
GATE2019 EE: 21
The $Y_{\text{bus}}$ matrix of a twobus power system having two identical parallel lines connected between them in pu is given as $Y_{\text{bus}} = \begin{bmatrix} j8 & j20 \\ j20& j8 \end{bmatrix}$The magnitude of the series reactance of each line in pu (round off upto one decimal place) is__________.
asked
Feb 12
in
new
by
Arjun
(
5.4k
points)
gate2019ee
numericalanswers
0
votes
0
answers
33
GATE2019 EE: 33
The enhancement type MOSFET in the circuit below operates according to the square law. $\mu _nC_{ox} =100 \: \mu A /V^2$, the threshold voltage $(V_T)$ is $500$ mV. Ignore channel length modulation. The output voltage $V_{\text{out}}$ is $100$ mV $500$ mV $600$ mV $2$ V
asked
Feb 12
in
new
by
Arjun
(
5.4k
points)
gate2019ee
0
votes
0
answers
34
GATE201842
As shown in the figure, $C$ is the arc from the point $(3,0)$ to the point $(0,3)$ on the circle $x^2+y^2=9$. The value of the integral $\int_C (y^2+2yx) dx +(2xy+x^2)dy$ is ________ (up to $2$ decimal places).
asked
Feb 19, 2018
in
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by
Arjun
(
5.4k
points)
gate2018ee
numericalanswers
0
votes
0
answers
35
GATE201843
Let $f(x) = 3x^37x^2+5x+6$. The maximum value of $f(x)$ over the interval $[0,2]$ is ________ (up to one decimal place).
asked
Feb 19, 2018
in
new
by
Arjun
(
5.4k
points)
gate2018ee
numericalanswers
0
votes
0
answers
36
GATE201819
In the twoport nework shown, the $h_{11}$ parameter $\bigg($ where, $h_{11} = \frac{V_1}{I_1}$, when $V_2=0 \bigg)$ in ohms is _________ (up to $2$ decimal places).
asked
Feb 19, 2018
in
new
by
Arjun
(
5.4k
points)
gate2018ee
numericalanswers
0
votes
0
answers
37
GATE2019 EE: 19
The current $I$ is flowing in the circuit shown below in amperes (round off to one decimal place) is _________
asked
Feb 12
in
new
by
Arjun
(
5.4k
points)
gate2019ee
numericalanswers
0
votes
0
answers
38
GATE201833
Consider a system governed by the following equations $ \frac{dx_1(t)}{dt} = x_2(t)x_1(t) \\ \frac{dx_2(t)}{dt} = x_1(t)x_2(t)$ The initial conditions are such that $x_1(0)<x_2(0)< \infty$. Let $x_{1f}= \underset{t \to \infty}{\lim} x_1(t)$ ... is true? $x_{1f}<x_{2f}<\infty$ $x_{2f}<x_{1f}<\infty$ $x_{1f}<=_{2f}<\infty$ $x_{1f}=x_{2f}=\infty$
asked
Feb 19, 2018
in
new
by
Arjun
(
5.4k
points)
gate2018ee
0
votes
0
answers
39
GATE201824
A separately excited dc motor has an armature resistance $R_a =0.05 \: \Omega$. The field excitation is kept constant. At an armature voltage of $100$ V, the motor produces a torque of $500$ Nm at zero speed. Neglecting all mechanical losses, the noload speed of the motor (in $\text{radian /s}$) for an armature voltage of $150$ V is ____________ (up to $2$ decimal places).
asked
Feb 19, 2018
in
new
by
Arjun
(
5.4k
points)
gate2018ee
numericalanswers
0
votes
0
answers
40
GATE201826
A transformer with toroidal core of permeability $\mu$ is shown in the figure. Assuming uniform flux density across the circular core crosssection of radius $r < < R$, and neglecting any leakage flux, the best estimate for the mean radius $R$ is $\frac{\mu V r^2 N_P^2 \omega}{I} \\ $ ... $\frac{\mu V r^2 N_P^2 \omega}{2I} \\ $ $\frac{\mu I r^2 N_P^2 \omega}{2V} $
asked
Feb 19, 2018
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Arjun
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5.4k
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gate2018ee
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